2023/06/27 by Jiming Ma, Ma, Jiming
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Algebra and Geometry #Amino Acid Enzymes and Metabolism #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2306.15127
openalex publication_date 2023/06/27 · openalex created_date 2023/06/30 · openalex updated_date 2026/07/28
We study the moduli space of discrete, faithful, type-preserving representations of the modular group PSL(2,ℤ) into PU(3,1). The entire moduli space M is a union of M(0,(2π)/(3),(4π)/(3)), M((2π)/(3),(4π)/(3),(4π)/(3)) and some isolated points. This is the first Fuchsian group such that its PU(3,1)-representations space has been entirely constructed. Both M(0,(2π)/(3),(4π)/(3)) and M((2π)/(3),(4π)/(3),(4π)/(3)) are parameterized by a square, where two opposite sides of the square correspond to representations of PSL(2,ℤ) into the smaller group PU(2,1). In particular, both sub moduli spaces M(0,(2π)/(3),(4π)/(3) ) and M((2π)/(3),(4π)/(3),(4π)/(3)) interpolate the geometries studied in \citeFalbelKoseleff:2002 and \citeFalbelparker:2003.